Exam - Erick Martins Ratamero





We can see that the system, no matter the starting point, converges to a cyclic oscillation with the configuration c=2 and b=0. The cycle is exactly the same no matter where the system started (only the way to get to the cycle is different).





Changing the value of c seems to make the shape different, as also the excursion on the vertical axis. The general behavior is kept.





Introducing a non-zero value for b also alters the shape and the excursions, this time on both axis. However, for small values of b, the general behavior stays the same, with the system converging to a cyclic oscillation.





Finally, by taking a b big enough, the system goes out of its "normal" behavior, and instead of converging to a cycle it seems to converge to a point. Note that, the same way the starting point would not influence the cycle, the starting point here does not seem to affect the point to where the system converges (in this case, something like (1.5, -0.38)).

The source code for the simulations (in Python, using RK4 for calculation) can be found below.